WMA11 October 2022

3.​​ WMA11/01 Edexcel IAL P1 October 2022, Q3​​ (Simultaneous​​ Equations)

The share price of a company is monitored.​​ 

Exactly 3 years after monitoring began, the share price was £1.05​​ 

Exactly 5 years after monitoring began, the share price was £1.65​​ 

The share price, £V, of the company is modelled by the equation​​ 

V = pt + q 

where t is the number of years after monitoring began and p and q are constants.​​ 

(a) Find the value of p and the value of q.​​ 

(3)

Exactly T years after monitoring began, the share price was £2.50​​ 

(b) Find the value of T, according to the model, giving your answer to one decimal place.​​ 

(2)

SOLUTION

a-​​ 

When​​ t=3 & v=1.05 

1.05=p3+q

3p+q=1.05     1

When​​ t=5 & v=1.65

1.65=p5+q

5p+q=1.65    2

Subtracting equation 1 from 2

2p=0.6 

p=0.3

Putting the value of p in any of the above equation (1) or (2)

3p+q=1.05

30.3+q=1.05

0.6+q=1.05

q=1.05-0.9

q=0.15

b-​​ Let​​ t=T​​ when​​ v=2.50. Putiing eh values in the given equation. Aalso subtitute the valuesi of p and q found in above part.

V=pt+q

V=0.3t+0.15

2.5=0.3T+0.15

2.5-0.150.3=T

T=7.8333….

T= 7.8 years